Coordinate unstable

A global property function is usually expressed as the expectation value of an operator or as the derivative of such an expectation value with respect to an internal or external parameter of the system. In the Born-Oppenheimer approximation, the electronic wave function depends parametrically upon the coordinates of the n nuclei, and therefore a set of the 3 -6 linearly independent nuclear coordinates constitutes the natural variables for such a choice of the potential function. However, the manifold M on which the gradient vector field is bound can be defined on a subset of 1R provided q < 3n-6, for example the intrinsic reaction coordinate (unstable manifold of a saddle point of index 1 of the Born-Oppenheimer energy hypersurface) or the reduced reaction coordinate. 

Since we assume different force constants, we can still have an accurate and stable solution for the second mode if At [Pg.445]

Ridge coordinate Unstable coord. Stable coord. Neutral coord. Ridge equation... 

For molecules with an even number of electrons, the spin function has only single-valued representations just as the spatial wave function. For these molecules, any degenerate spin-orbit state is unstable in the symmetric conformation since there is always a nontotally symmetric normal coordinate along which the potential energy depends linearly. For example, for an - state of a C3 molecule, the spin function has species da and E that upon... 

Den Otter, W.K., Briels, W.J. The reactive flux method applied to complex reactions using the unstable normal mode as a reaction coordinate. J. Chem. Phys. 106 (1997) 1-15. 

Pd(II) compounds coordinate to alkenes to form rr-complexes. Roughly, a decrease in the electron density of alkenes by coordination to electrophilic Pd(II) permits attack by various nucleophiles on the coordinated alkenes. In contrast, electrophilic attack is commonly observed with uncomplexed alkenes. The attack of nucleophiles with concomitant formation of a carbon-palladium r-bond 1 is called the palladation of alkenes. This reaction is similar to the mercuration reaction. However, unlike the mercuration products, which are stable and isolable, the product 1 of the palladation is usually unstable and undergoes rapid decomposition. The palladation reaction is followed by two reactions. The elimination of H—Pd—Cl from 1 to form vinyl compounds 2 is one reaction path, resulting in nucleophilic substitution of the olefinic proton. When the displacement of the Pd in 1 with another nucleophile takes place, the nucleophilic addition of alkenes occurs to give 3. Depending on the reactants and conditions, either nucleophilic substitution of alkenes or nucleophilic addition to alkenes takes place. 

Iron hahdes react with haHde salts to afford anionic haHde complexes. Because kon(III) is a hard acid, the complexes that it forms are most stable with F and decrease ki both coordination number and stabiHty with heavier haHdes. No stable F complexes are known. [FeF (H20)] is the predominant kon fluoride species ki aqueous solution. The [FeF ] ion can be prepared ki fused salts. Whereas six-coordinate [FeCy is known, four-coordinate complexes are favored for chloride. Salts of tetrahedral [FeCfy] can be isolated if large cations such as tetraphenfyarsonium or tetra alkylammonium are used. [FeBrJ is known but is thermally unstable and disproportionates to kon(II) and bromine. Complex anions of kon(II) hahdes are less common. [FeCfy] has been obtained from FeCfy by reaction with alkaH metal chlorides ki the melt or with tetraethyl ammonium chloride ki deoxygenated ethanol. 

Carbon monosulfide [2944-05-0] CS, is an unstable gas produced by the decomposition of carbon disulfide at low pressure ia a silent electrical discharge or photolyticaHy (1 3) ia the presence or absence of sulfur (3). It decomposes with a half-life of seconds or minutes to a black soHd of uncertain composition (1—3). The monosulfide can be stabilized ia a CS2 matrix at — 196°C, and many stable coordination complexes of CS with metals have been prepared by iadirect means (8). 

Coordination Complexes. The coordination and organometaHic chemistry of thorium is dominated by the extremely stable tetravalent ion. Except in a few cases where large and stericaHy demanding ligands are used, lower thorium oxidation states are generally unstable. An example is the isolation of a molecular Th(III) complex [107040-62-0] Th[Tj-C H2(Si(CH2)3)2]3 (25). Reports (26) on the synthesis of soluble Th(II) complexes, such as... 

Electrophilic attack on ring heteroatoms ties up an electron pair (which may have been engaged in resonance in the parent species) and confers positive charge on the system, thereby inviting nucleophilic attack or elimination reactions to follow. In small systems the primary product is usually quite unstable. Nucleophilic attack on protonated or Lewis acid-coordinated species will be treated below (Section 5.2.7), because it is not always clear whether such reactions are preceded by an electrophilic step (e.g. protonation) or not. 

The situation simplifies when V Q) is a parabola, since the mean position of the particle now behaves as a classical coordinate. For the parabolic barrier (1.5) the total system consisting of particle and bath is represented by a multidimensional harmonic potential, and all one should do is diagonalize it. On doing so, one finds a single unstable mode with imaginary frequency iA and a spectrum of normal modes orthogonal to this coordinate. The quantity A is the renormalized parabolic barrier frequency which replaces in a. multidimensional theory. In order to calculate... 

Intramolecular chalcogen interactions may also stabilize reactive functional groups enabling the isolation of otherwise unstable species or their use as transient intermediates, especially in the case of selenium and tellurium. For example, tellurium(II) compounds of the type ArTeCl are unstable with respect to disproportionation in the absence of such interactions. The diazene derivative 15.23 is stabilized by a Te N interaction. Presumably, intramolecular coordination hinders the disproportionation process. Other derivatives of the type RTeX that are stabilized by a Te N interaction include 8-(dimethylamino)-l-(naphthyl)tellurium bromide, 2-(bromotelluro)-A-(p-tolyl)benzylamine, and 2-[(dimethylammo)methyl]phenyltellunum iodide. Intramolecular donation from a nitrogen donor can also be used to stabilize the Se-I functionality in related compounds." ... 

Figure 5-3 is the reaction coordinate diagram for Fig. 5-2. Note the region of the maximum potential energy on the reaction coordinate this region assumes great importance in kinetic theory. At this point the reacting system is unstable with respect to motion along the reaction coordinate. However, at this same point the system possesses minimum energy with respect to motion along dashed line cd. This portion of the reaction coordinate is called the transition state of the reaction. (This concept was introduced in Fig. 1-1.)...

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

In the vast majority of its compounds Si is tetrahedrally coordinated but sixfold coordination also occurs, and occasional examples of other coordination geometries are known as indicated in Table 9.2 (p. 335). Unstable 2-coordinate Si has been known for many years but in 1994 the stable, colourless, crystalline silylene [ SiNBu CH=CHNBu j, structure (1), p. 336, was... 

Cyclobutadiene complexes afford a classic example of the stabilization of a ligand by coordination lo a metal and, indeed, were predicted theoretically on this basis by H. C. Longuei-Higgins and L, E, Orgel (1956) some 3y before the first examples were synthesized, In the (hypothetical) free cyclobutadiene molecule 2 of the 4 rr-electrons would occupy t /i and there would be an unpaired electron m each of the 2 degenerate oibilals 2, Coordination to a metal provides funhei interactions and avoids this unstable configuration, See also the discussion on ferra-boranes (p. 174). 

The simplest of the ir-bondcd Re-C compounds is the green, paramagnetic, crystalline, therm ly unstable ReMen, w ich, after WMe, was only the second hexamethyl transition metal compound to be synthe zed 11976). It reacts with LiMe to give the unstable, pyrophoric, Lii[ReMe(,, which has a square-antiprismatic structure, and incorporation of oxygen into the coordination sphere greatly H reases the stability, wit e,ss Re CMe, which is thermally stable up to 200 C, and Re "0[Pg.1068]

The distinction between the first member of the group and the two heavier members, which was seen to be so sharp in the early groups of transition metals, is much less obvious here. The only unsubstituted, discrete oxoanions of the heavier pair of metals are the tetrahedral [Ru 04] and [Ru 04]. This behaviour is akin to that of iron or, even more, to that of manganese, whereas in the osmium analogues the metal always increases its coordination number by the attachment of extra OH ions. If RUO4 is dissolved in cold dilute KOH, or aqueous K2RUO4 is oxidized by chlorine, virtually black crystals of K[Ru 04] ( permthenate ) are deposited. These are unstable unless dried and are reduced by water, especially if alkaline, to the orange... 

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